It's actually pretty simple to use the event for this. Assign an id to the group and to the button inside the group (in the Properties panel).
Right click on the group on stage and select Add event...
Select Mouse > Mouseover event
Select CSS > Set styles as the action
Select the button id (displayed as group id button id) as the target.
Click on Add property button and set the CSS property, such as background-color, tab and assign the background color such as a hex value for the color such as #ff0000.
Click OK to save.
Hope it helps.
Google Web Designer team